Volume 9, issue 1 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Maps to the projective plane

Jerzy Dydak and Michael Levin

Algebraic & Geometric Topology 9 (2009) 549–568
Abstract

We prove the projective plane P2 is an absolute extensor of a finite-dimensional metrizable space X if and only if the cohomological dimension mod 2 of X does not exceed 1. This solves one of the remaining difficult problems (posed by A N Dranishnikov) in Extension Theory. One of the main tools is the computation of the fundamental group of the function space Map(Pn, Pn+1) (based at the inclusion) as being isomorphic to either 4 or 2 2 for n 1. Double surgery and the above fact yield the proof.

Keywords
absolute extensor, cohomological dimension, covering dimension, extension dimension, extension of maps, projective space
Mathematical Subject Classification 2000
Primary: 54F45
Secondary: 54C65, 55M10
References
Publication
Received: 4 April 2007
Revised: 22 February 2009
Accepted: 23 February 2009
Published: 30 March 2009
Authors
Jerzy Dydak
Department of Mathematics
University of Tennessee
Knoxville, TN 37996-1300
United States
http://www.math.utk.edu/~dydak
Michael Levin
Department of Mathematics
Ben Gurion University of the Negev
P.O.B. 653
Be’er Sheva 84105
Israel